We propose an approximation to full relativity that captures the main gravitational effects of dynamical importance in supernovae. The conceptual link between this formalism and the Newtonian limit is such that it could likely be implemented relatively easily in existing multidimensional Newtonian gravitational hydrodynamics codes employing a Poisson solver. As a test of the formalism's utility, we display results for rapidly rotating (and therefore highly deformed) neutron stars
